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Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration

  • The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which corrects both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.

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Metadaten
Author:Gilles BlanchardGND, Peter Mathe
DOI:https://doi.org/10.1088/0266-5611/28/11/115011
ISSN:0266-5611 (print)
Parent Title (English):Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Language:English
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Volume:28
Issue:11
Pagenumber:23
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert